1. Simplify
= 2
= 4
= 5
= 10
= 12

2. Objective - To simplify rational and irrational square roots.
List of Perfect Squares

3. Objective - To simplify irrational roots.
Example:
Check using a calculator!

4. Simplify. To simplify the number by hand
must have a perfect square factor.
No perfect
square factors
Can’t be
simplified

5. Simplify each irrational root.1) 4) 2) 5) 3) 6)

6. Simplify.
Perfect square

7. Simplify each irrational root.1) 4)
Already
Simplified 2) 5) 3) 6)

8. Ex. 1 Simplify

9. Ex. 2 Simplify

10. Radicals with Variables
To simplify radicals with variables: divide even exponents by 2; for odd exponents, pull out the largest even exponent, take the square root of that, and leave the remainder under the radical.

11. Radicals with Variables
Ex. 10 Even
Radicals with Variables

12. Radicals with Variables
Ex. 11 Odd
Radicals with Variables

13. + Combine Like Radicals
Miller
Miller
To combine radicals: combine the coefficients of like radicals. They must have the same last name.

14. Ex. 3 Simplify
Your Turn

15. Ex. 4
Simplify, then combine.

16. Ex. 5
Simplify, then combine.

17. Example The greatest perfect square factor of 96a4b is 16a4.
Use the product rule of square roots to separate the factors into two radicals.
Find the square root of 16a4 and leave 6b in the radical.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

18. Example Solution The greatest perfect square factor of 32x5 is 16x4.
Use the product rule of square roots to separate the factors into two radicals.
Find the square root of 16x4 and leave 2x in the radical.

19. Multiply Radicals *
To multiply radicals: multiply everything, then simplify.

20. Ex. 6
Multiply, then simplify.

21. Squared and Square Root Cancel
Ex. 7
Squared and Square Root Cancel

22. Dividing Radicals
To divide radicals: reduce or divide what you can and rationalize the denominator. A square root CANNOT be in the denominator.

23. Reduce or divide, then rationalize.
Ex. 8
Reduce or divide, then rationalize.

24. Ex. 9